Problem: Write the equation of a line that is perpendicular to $y=-x-6$ and that passes through the point $(-9,-4)$.
Getting started Key idea: The slopes of perpendicular lines are negative reciprocals of each other. Step 1: Find the slope Slope of the given line: ${-1}$ So, the slope of the perpendicular line: $C{\dfrac{1}{1}=1}$ Step 2: Substitute the known point into linear equation The perpendicular line will have a slope of $C{1}$ and pass through the point ${(-9,-4)}$. Let's start from the point-slope form of the equation of the perpendicular line, then solve for $y$. [What is the point-slope form?] $\begin{aligned} y-{(-4)} &= C{1}(x-{(-9)})\\\\\\ y+4 &= x +9 \\\\\\ y &=x {+5} \end{aligned}$ Answer $y=x {+5}$. ${2}$ ${4}$ ${6}$ ${8}$ ${\llap{-}4}$ ${\llap{-}6}$ ${\llap{-}8}$ ${2}$ ${4}$ ${6}$ ${8}$ ${\llap{-}4}$ ${\llap{-}6}$ ${\llap{-}8}$ $y$ $x$